This disclosure is related generally to the field of geophysical surveying, and more specifically to acquiring ghost-free or near-ghost free data. The disclosure may have applications in the field of broadband source calibration. The disclosure may have benefit when applied to marine surveying operations.
A signature of a seismic source (e.g., an air gun or an air gun array) can be modeled using conventional approaches. Such modeling can be used to indentify noise components when the seismic source is used to perform a seismic survey. However, the advent of broadband marine seismic solutions unveils limitations in conventional modeling approaches outside the marine seismic bandwidth.
While a farfield signature of an air gun array can be modeled using approaches based on Rayleigh's theory of oscillating bubbles, broadband marine seismic solutions may unveil limitations in modeling algorithms outside marine seismic bandwidth. There are several reasons for this that can stem from implementations of source modeling procedures.
Conventional approaches to source modeling may fail to take into account higher frequencies. For example, in many cases the Digital Field System V (DFS-V) Out-128 (72) Hz (decibel/octave) filter may be used for filtering to compare measured and modeled signatures of an air gun. As a consequence, models calibrated according to this approach may not perform outside the frequency range of the DFS-V filter. Measured signatures that were used for calibration could include a source ghost, which could mask frequency ranges depending on a depth of a shot from a seismic source (e.g., an air gun). Within these masking limits, modeling schemes may be devised that could match array signatures well enough to be used in de-signature applications.
As interest in wider frequency ranges grows, the previously masked information can become useful. Modeled signatures that depend on filter systems with a defined calibration range can become less reliable outside the calibration range. Approaches to broaden the applicable frequency range beyond conventional calibration ranges include both calibrating over a broader bandwidth, as well as improving the underlying model such that deviations from calibrated values can be handled.
Marine seismic air gun modeling can be, for example, based on the dynamics of an oscillating air bubble created by an underwater explosion. Some energy loss during the bubble oscillation can be due to mass transfer inside the bubble. As the bubble oscillates, water may evaporate at the bubble wall and condense inside the bubble to produce a transfer of mass of water into the bubble, causing the dampening exhibited in bubble pulses of an air gun signature. The exact rate at which these processes work can be difficult to describe theoretically due to strong variations of temperature and pressure inside the air bubble. As a result, observed rates can be used as calibration in order to make modeled signatures fit recorded data. This may be sufficient for a good fit with a specific (narrow) bandwidth specification; however, it may not be accurate enough for modeling of broadband signatures.
Other physical effects may contribute to differences between measured and modeled signatures. Such effects can be part of the source modeling theory. This can include a realistic model of air escaping from a seismic source (e.g., an air gun) to describe the shape of a primary pulse, and upward movement of the bubble due to buoyancy. As longer time signatures are used for processing, effects of upward movement of the bubble due to buoyancy can be increasingly important.
There may also be high-frequency effects that are not directly reproducible, such as cavitation. While such noise may not be especially relevant in a broadband frequency range, it may be beneficial for purposes such as modeling environmental effects.
In addition to the dynamics of each air bubble, seismic sources (e.g., air guns) may also interact with each other. While some interaction between air guns can be known, the case of clusters, for example, where air bubbles of two or more air guns coalesce, may be less clear. Two-gun clusters have been researched and can be used in array designs. However, in searching for low frequencies, hyperclusters, which are beyond the scope of both the original model and the original calibration of existing modeling algorithms, may be used.
Therefore, higher accuracy in modeling seismic source signatures is desired.
To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. It is contemplated that elements disclosed in one embodiment may be beneficially utilized on other embodiments without specific recitation.